Dynamics of Coupled Quantum-Classical Oscillators

The dynamics of systems consisting of coupled quantum-classical oscillators is numerically investigated. It is shown that, under certain conditions, the quantum oscillator exhibits chaos. When the mass of the classical oscillator increases, the chaos will be suppressed; if the energy of the system and/or the coupling strength between the two oscillators increases, chaotic behaviour of the system appears. This result will be helpful to understand the probability of the emergence of quantum chaos and may be applied to explain the spectra of complex atoms qualitatively.     

Numerical Investigation for the Properties of Nonintegrable Quantum SYstems Eigenspace in the Line of Quantum—Classical Correspondence

The properties of the eigenspace of nonintegrable quantum systems are explored in detail in the light of the viewpoint of quantum-classical completely correspondence proposed recently by Xu et al.The changes of the topological structure in the state space of autonomous quantum system due to the nonlinear resonance are displayed numerically with the uncertainty measure of a special initial state ρα（λ） and the transformation matrix U(λ δλ-λ-δλ）,The statistical behavior of the subspace occupied by the state in eigenspace of quantum nonintegrable system is discussed carefully with the help of a special renormalization method.The results show that the randomness of effective Hamilonian matrix,the transition matrix and the nearest level spacings in this region can be described by random matrix theory.And the extent of agreement of our calculation with the prediction of GOE is in correspondence to the extent of the classical torus violation.     

Quantum Statistics of a Forced Oscillator with a Time－Dependent Driving Force

Quantum statistics of a forced harmonic oscillator acted upon by a time-dependent external force are derived usingthe Wilcox trick and the time-dependent inhomogeneous Bogoliubov transformation formalism. The internal energy, fluctuation of the particle-number average and entropy of this nonequilibrium system are presentedexplicitly.     

The Electron－Hole Pair in a Single Quantum Dot and That in a Vertically Coupled Quantum Dot

The energy spectra of low-lying states of an exciton in a single and a vertically coupled quantum dots are studied under the influence of a perpendicularly applied magnetic field. Calculations are made by using the method of numerical diagonalization of the Hamiltonian within the effective-mass approximation. We also calculated the binding energy of the ground and the excited states of an exciton in a single quantum dot and that in a vertically coupled quantum dot as a function of the dot radius for different vaJues of the distance and the magnetic field strength.     

Multiparty Quantum Secret Sharing of Classical Message using Cavity Quantum Electrodynamic System

An experimental feasible scheme of multiparty secret sharing of classical messages is proposed, based on a cavity quantum electrodynamic system. The secret messages are imposed on atomic Bell states initially in the sender＇s possession by local unitary operations. By swapping quantum entanglement of atomic Bell states, the secret messages are split into several parts and each part is distributed to a separate party. In this case, any subset of the entire party group can not read out the secret message but the entirety via mutual cooperations. In this scheme, to discriminate atomic Bell states, additional classical fields are employed besides the same highlydetuned single-mode cavities used to prepare atomic Bell states. This scheme is insensitive to the cavity decay and the thermal field, and usual joint Bell-state measurements are unnecessary.     

Two-Variable Hermite Function as Quantum Entanglement of Harmonic Oscillator＇s Wave Functions

We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S（γ）Hm,n （μa1^＋, μa2^＋│00〉, which is the minimum uncertainty state for sum squeezing, in （ η│representation is calculated.     

Fisher Information of Wavefunctions： Classical and Quantum

A parametric quantum mechanical wavefunction naturally induces parametric probability distributions by taking absolute square, and we can consider its classical Fisher information. On the other hand, it also induces parametric rank-one projections which may be viewed as density operators, and we can talk about its quantum Fisher information. Among many versions of quantum Fisher information, there are two prominent ones. The first, defined via a quantum score function, was introduced by Helstrom in 1967 and is well known. The second, defined via the square root of the density operator, has its origin in the skew information introduced by Wigner and Yanase in 1963 and remains relatively unnoticed. This study is devoted to investigating the relationships between the classical Fisher information and these two versions of quantum Fisher information for wavefunctions. It is shown that the two versions of quantum Fisher information differ by a factor 2 and that they dominate the classical Fisher information. The non-coincidence of these two versions of quantum Fisher information may be interpreted as a manifestation of quantum discord. We further calculate the difference between the Helstrom quantum Fisher information and the classical Fisher information, and show that it is precisely the instantaneous phase fluctuation of the wavefunctions.     

Sommerfeld＇s Quantum Condition of Action and the Spectra of Quantum Schwarzschild Black Hole

If the situation of quantum gravity nowadays is nearly the same as that of quantum mechanics in its early time of Bohr and Sommerfeld, then a first-step study of the quantum gravity under Sommerfeld‘s quantum condition of action might be helpful. We present the spectra of quantum Schwarzschild black hole in non-relativistic quantum mechanics. It is found that the quantum of area is 8π/3 lp^2, the quantum of entropy is 2π/4kB, and the Hawking evaporation will cease when the black hole reaches the ground state m=1/2√3mp.     

Effect of Noise on Berry‘s Phase for Quantum Computing

Based on a new type of two-level-system reservoir, we investigate the impact of dissipation on Berry‘‘s phase of a spin trapped in a periodical external field. It is found that the existence of environmental noise could lead to a decaying term in the matrix of Berry‘s phase as the sign of a decoherence process, which is in agreement with the result of Nazir et al. (Phys. Rev. A 65 (2002) 042303). Particularly, in comparison with a specialized case of the traditional Leggett dissipation model, we only shows the dependence of time but not temperature in decaying tem. A concrete case is exhibited by using the one-dimensional Ohmic function.     

Quantum Fluctuation of Mesoscopic Capacitance Coupled Circuit in a Thermal Vacuum State

The quantum fluctuations of mesoscopic capacitance-coupled circuit in thermal vacuum state are investigated by using the theory of thermal field dynamics on the basis of quantization of the mesoscopic circuit. It is shown that under a definite temperature, the fluctuations of electric charges and currents change with temperature. The higher the temperature, the more quantum noise the coupled circuit exhibits.     

Quantum fluctuation dynamics in momentum spread of cold atoms

Dynamics of the qaanturn system Lhat 0msLsts d a cold atom in a moclulated standing wave of light is analyzed using the time-depmdmt variaticnal principle formulation based on squeezed coherent states. A group of ordinary differential equations describing evolutioa of two pairs of canonically conjugate variables(q(t),p(t):G(t),II(t)) are derived where G(t) and II(t) describe the quantum fluctuations of the system,It has been shown that a transition from the regular motion to the chaotic motion in G(t),II(t) phase space.Quantum system seems to be capable to show the classical-like chaotic structure.     

Quantum Poincare Section of a Two—Dimensional Hamiltonian in a Coherent State Representation

We study the quantum behaviour of a quasi-integrable Hamiltonian.The unperturbed Hamiltonian displays degeneracies of energy levels,which become avoided crossing under a nonintegrable perturbation.In this two-dimensional system,the quantum Poincare section plot is constructed in the coherent state representation with the restriction that the centres of the wavepackets are confined at thd classical surface of constant energy.It is found that the quantum Poincare section plot obtained in this way provides an evident counterpart of the classical system.     

Quantum—Confined Stark Effect of Vertically Stacked Self—Assembled Quantum Discs

We study the electronic energy levels and probability distribution of vertically stacked self-assembled InAs quantum discs system in the presence of a vertically applied electric field. This field is found to increase the splitting between the symmetric and antisymmetric levels for the same angular momentum. The field along the direction from one disc to another affects the electronic energy levels similarly as that in the opposite direction because the two discs are identical. It is obvious from our calculation that the probability of finding an electron in one disc becomes larger when the field points from this disc to the other one.     

Quantum Spectra and Classical Orbits in Two-Dimensional Equilateral Triangular Billiards

We study the correspondence between quantum spectra and classical orbits in the equilateral triangular billiards. The eigenstates of such systems are not separable functions of two variables even though the problem is exactly solvable. We calculate the Fourier transform of a quantum spectral function and find that the positions of the peaks match well with the lengths of the classical orbits. This is another example showing that the quantum spectral function provides a bridge between quantum and classical mechanics.     

Quantum Dynamics of One—Dimensional Nanocrystalline Solids

A novel ballistic-nonballistic dynamic transition in one-dimensional nanocrystalline solids is found upon varying the strength of the composition modulation and the grain-boundary effect.This can contribute to the understanding of the strange electronic transport porperties of nanostructured systems.